Packed planes and a high volume of carry-ons are forcing airlines to expand the space above a passenger’s head. United and Delta are the latest airlines to replace or upgrade bins so they hold more luggage. And engineers at Boeing are designing jet interiors with today’s bulkier luggage in mind.

It’s a chance to placate passengers who feel like they’re thrown into a roller derby every time they board a plane. Because of fees on checked bags, more passengers are bringing carry-ons, which are growing in size. And with planes more crowded than ever, bins fill up before everyone has reached their seat. Travelers fight physics and one another to shove one more bag overhead. Or they’re forced to check luggage at the gate.

The result is upset travelers, harried flight attendants and delays.

The percentage of passengers bringing bags on board has hovered around 87 percent in recent years, United Continental says. And “the size of the carry-on has increased … They are stretching the limits of their bags,” says Scott O’Leary, managing director of customer solutions at United Continental Holdings Inc.

Expanding bins is a smart way for airlines to set themselves apart, says Henry Harteveldt, who leads airline and travel analysis at Atmosphere Research Group, a market research firm. “Especially if they cater to the business traveler, they’re hoping it will give them a small but noticeable competitive advantage.”

Business travelers, for example, avoid an airline that doesn’t have room for their carry-ons.

At first blush, it might seem like airlines risk giving away fees if more people can fit carry-ons on board. But they’re not risking much as it turns out.

Airlines often waive bag fees when luggage can’t fit overhead and must be checked at the gate. And business travelers, who generate most of the industry’s revenue, are often exempt from baggage fees anyway.

But will bigger bins encourage fliers to bring larger bags? Airlines hope not, and are trying to crack down before luggage makes it into the cabin.

Airlines expanding their bins include:

United: The airline is replacing bin doors on 152 planes starting in April. The new doors curve out more than the old ones. That allows passengers to slide bags into the compartment wheels-first instead of sideways. The renovated bins will be on all of United’s Airbus A320s, one of the main jets the airline uses for domestic flying. The planes will hold 106 typical roll-on bags, up from 64. The bins are also getting more rugged latches because latches on overstuffed bins are more likely to break.

Passengers on United’s A320s have had to check their bags at a higher rate than travelers on other planes because there wasn’t enough room. “That’s a real sore point,” O’Leary says.

American Airlines: The airline’s new 737s will hold 48 more bags than the planes they are replacing, although they have 24 more seats, too. That means more people and luggage. American’s older 737s are also getting new baggage-bin doors that curve out more. The work is finished on about half of the 76 planes.

Delta Air Lines: Passengers on international routes like Atlanta-Paris or Minneapolis-Amsterdam are starting to see new bins on the airline’s 767 jets. The compartments hold 26 more bags than the bins they are replacing. It’s an increase of 23 percent.

US Airways Group Inc.: In 2008, it enlarged bins on its 757s, a mid-sized plane flown on routes including Phoenix to Hawaii and Charlotte, N.C., to Dublin. Like United, the change allowed fliers to slide bags in wheels-first instead of sideways. “We know it’s a customer enhancement, and yeah, they like it,” says US Airways spokeswoman Michelle Mohr.

Tim Kirkwood, a flight attendant for 35 years, remembers overhead bins that were basically open shelves for coats and hats. Now, leisure travelers trying to avoid a bag fee will bring as much as they can into the cabin.

“A bigger bin is good because at least more stuff will fit up there,” says Kirkwood, who asked that his airline not be identified. “But it just seems to encourage them to bring more stuff.”

Boeing wants its new planes to have the right bins for all that stuff.

The company is engineering its bins to be a better fit for a standard 9 x 14 x 22-inch roll-aboard bag. That’s a change from the past. Designers used to focus on maximizing cubic inches. That produced impressive-sounding space that would be quoted in Boeing’s sales materials. But it wasn’t necessarily a good fit for actual carry-on luggage, says Kent Craver, Boeing’s cabin expert.

“We never used to talk about how many bags would fit. We talked about volume,” he says.

In designing bins on its new 787, Boeing dispatched workers to Costco and other stores to buy roll-aboard bags to make sure they would fit. The 787-8 holds 10 percent more carry-on bags than the larger 777, even though the volume inside the bins is about the same.

For passengers, “volume doesn’t really matter. It’s whether or not my bag fits,” Craver says. And that’s the number Boeing now shows in its sales materials.

The extra space also makes it more likely that bags will end up close to the passenger who brought them.

“They don’t want it 20 rows behind them or 20 rows in front of them, because that causes a lot of anxiety,” Craver says.

Bigger bins help. So would passengers who follow the rules about carry-on sizes.

Passengers with bigger-than-allowed bags might take bin space from others. It can be tough for airlines to enforce the rules with passengers who print their own boarding pass at home. That’s because the first time an airline worker sees them is at the gate.

United is trying to be stricter about carry-on sizes. It has been running an experiment at a few airports, where agents are told to look out for bags that are too big or passengers who bring too many. Oversized bags are checked at the gate. As a result, there’s more room to stow carry-ons. United declined to identify the airports.

American is also trying to be tougher about carry-on sizes. At every gate, it has installed new size-checking boxes with three hard sides. Bags either slide in or they don’t. The old checkers had no walls, so it was easier to fudge. Airline spokesman Tim Smith says the new boxes act as an arbiter when customers deny that their carry-on is too bulky. American will check a bag for free at the gate if it’s too big.

Emily Quinnell, who studies social work at the University of Wisconsin-Madison, had to check some small bags at the gate on a recent flight between Minneapolis and Denver. There was no room in the bins. She says airlines should have known that charging for luggage would cause passengers to push the limits of what they can bring on board.